Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;


public class Main111 {
    public static void main(String[] args) {
        
        Scanner in = new Scanner (System.in);
        
        int n=in.nextInt();
      
        ArrayList<Integer> list = new ArrayList<>();
        list.add(1);
        
        for (int i = 1; i <=n; i++)
        {
            int x=list.get(i-1)+(i+1);
            if(x>n)break;
            list.add(x);
        }
        
        
     
        int i=0,j=list.size()-1;
        while(i<list.size())
        {
            while(list.get(i)+list.get(j)>n&&j>0)j--;
            if(list.get(i)+list.get(j)==n)
            {
                System.out.println("YES");
                return;
            }
            i++;
        }
        
        System.out.println("NO");
        
        
        
        
    }
   
}